Two-weight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions

We investigate a generalized spherical means operator, viz. generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of the corresponding kernel. As the main result, we prove two-weight mixed norm estimates for the integral operator, with general power weights involved. This leads to weighted Strichartz type estimates for solutions to certain Cauchy problems for classical Euler-Poisson-Darboux and wave equations with radial initial dataMTM2015-65888-C4-4-P Leonardo Foundation grant for Investigadores y Creadores Culturales 2017 from BBV

Maximal estimates for a generalized spherical mean Radon transform acting on radial functions

We study a generalized spherical means operator, viz. generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associated maximal operator and its local variant to be bounded on power weighted Lebesgue spaces. This translates, in particular, into almost everywhere convergence to radial initial data results for solutions to certain Cauchy problems for classical Euler-Poisson-Darboux and wave equations. Moreover, our results shed some new light to the interesting and important question of optimality of the yet known $L^p$ boundedness results for the maximal operator in the general non-radial case. It appears that these could still be notably improved, as indicated by our conjecture of the ultimate sharp result.Comment: 20 pages, 2 figures. Sharpness results added and minor things improved or corrected. Accepted for publication in Annali di Matematica Pura ed Applicat

Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functions

We investigate a generalized spherical means operator, in other words the generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of the corresponding kernel. As the main result, we prove two-weight mixed norm estimates for the integral operator, with general power weights involved. This leads to weighted Strichartz-Type estimates for solutions to certain Cauchy problems for classical Euler{Poisson{Darboux and wave equations with radial initial data. © 2017 Society for Industrial and Applied Mathematics

Bilinear Bochner-Riesz square function and applications

In this paper we introduce Stein's square function associated with bilinear Bochner-Riesz means and develop a systematic study of its $L^p$ boundedness properties. We also discuss applications of bilinear Bochner-Riesz square function in the context of bilinear fractional Schr\"{o}dinger multipliers, generalized bilinear spherical maximal function and more general bilinear multipliers defined on $\mathbb{R}^{2n}$ of the form $(\xi,\eta)\rightarrow m\left(|(\xi,\eta)|^2\right)$.Comment: Comments are welcom